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Monthly Archives: September 2016
Writing Probability as an Expectation (10/365)
Expectation is such an ubiquitous construct in probability that it’s worth looking at the various situations in which it appears. It’s one of those constructs that was so cheap to invent but pays off time and again. Consider a random … Continue reading
Online Mean Variance (9/365)
I am uploading a module I had written to compute the mean and the estimated variance in a streaming fashion as described here. I’ve wrapped it in a Monoid for convinence. The module can be found here. ghci> :l OMVar.lhs … Continue reading
Correlation – III, Linear Dependence (8/365)
In a previous post, I showed one way to arrive at the correlation coefficient but it doesn’t really convince me of its need. What follows is a derivation that will show you a more direct meaning for the correlation coefficent … Continue reading
Correlation – II (7/365)
In the last post, I said I’d give an example of two random variables whose expectations are independent but are not themselves independent. For a first attempt, this turned out not to be an easy task because when coming up … Continue reading
Correlation – I (6/365)
Let me follow up on the theme – talked about here – of distributing an operator over another. To recap, we saw two ways of distributing an expectation Can we say anything like this about variance? Consider the variance of … Continue reading
Dealing with Dates and Times (5/365)
In the past, I’ve had to deal with reading, writing, and performing arithmetic on dates and times in Haskell and the experience is not a pleasant one. Actually, I’ve had to do this in PHP and Erlang and the experience … Continue reading
Product of Expectations (4/365)
Suppose you invent a function that operates on some domain . An incredibly fruitful exercise in mathematics is to try and see if distributes in some way over some operator in the domain. Consider these familiar examples. ; multiplication distributes … Continue reading
What happens if we use absolute value? (3/365)
Yesterday, I looked at how the mean minimizes the variance and how this happened due to defining the variance as the mean of the square of the differences (also known as the norm). In particular, replacing the square with higher … Continue reading
How are mean and variance related? (2/365)
I’ve recently been working through the problems in the book Probability by A. N. Shiryayev. I’ll probably end up posting some answers to interesting exercises here as I go through them. Regrettably, although I did take many math courses at … Continue reading
Starting Daily Posts! (1/365)
Many authors of blogs I follow have – as a way of getting into the flow of writing – committed to writing a post a day for a year. You’ll see a counter like (112/365) in the title of each … Continue reading